And the priest shall burn them upon the altar
Which shows that not the fat only, but the inwards and the kidneys, were burnt also; so Maimonides says F12, that the priest salted the parts, and burned them upon the altar; and the priests might not have the breast and shoulder (which were what belonged to them) until the parts were burnt:
[it is] the food of the offering made by fire;
which the Lord ate of, or accepted of:
for a sweet savour;
as a type of the sweet smelling sacrifice of Christ, with which he is well pleased;
all the fat is the Lord's;
that is, all that was upon the parts mentioned in the several sacrifices of peace offerings, which was to be taken off and burnt: though the Jewish writers understand it of all fat in general, and so interpret the law that follows.